Radiative transfer (RT) in spectral lines in plasmas and gases under complete redistribution of the photon frequency in the emission-absorption act is known as a superdiffusion transport characterized by the irreducibility of the integral (in the space coordinates) equation for the atomic excitation density to a diffusion-type differential equation. The dominant role of distant rare flights (Lévy flights, introduced by Mandelbrot for trajectories generated by the Lévy stable distribution) is well known and is used to construct approximate analytic solutions in the theory of stationary RT (the escape probability method is the best example). In the theory of nonstationary RT, progress based on similar principles has been made recently. This includes approximate self-similar solutions for the Green’s function (i) at an infinite velocity of carriers (no retardation effects) to cover the Biberman–Holstein equation for various spectral line shapes; (ii) for a finite fixed velocity of carriers to cover a wide class of superdiffusion equations dominated by Lévy walks with rests; (iii) verification of the accuracy of above solutions by comparison with direct numerical solutions obtained using distributed computing. The article provides an overview of the above results with an emphasis on the role of distant rare flights in the discovery of nonstationary self-similar solutions.

The accuracy of approximate automodel solutions for the Green’s function of the Biberman-Holstein equation for the Stark broadening of spectral lines is analyzed using the distributed computing. The high accuracy of automodel solutions in a wide range of parameters of the problem is shown.

A statistical analysis is carried out of the similarity of profiles of plasma parameters: electron temperature T _e, density n _e, and pressure P _e, at the stage of quasi-stationary plasma current (the so called flat-top stage) of about 9000 discharges in the JET tokamak, among the discharges from #84458 to #99419 that covers almost the entire database of successful discharges in the JET ITER-like wall machine. For all these parameters, the existence of universal profiles is shown as functions of the normalized minor radius of the plasma column ρ. The discharge universal profiles (DUPs) are obtained by dividing the space-time-dependent profile by its value at the center of the plasma column or by the space-averaged value of this parameter in the region ρ ⩽ ρ _max = 0.5–1, and subsequent averaging over time at the flat-top stage of each discharge. The machine universal profiles (MUPs) are obtained by averaging over time of flat-top stage of all discharges. It is shown that for 86% of the discharges, the time-averaged relative root-mean-square deviation of P _e profile from the DUP is less than 20% at ρ ⩽ 0.8, and for the MUP, it is less than 17%. A similar picture is observed for the profiles of T _e and n _e/√T _e. An auxiliary heating, P _aux ⩾ 1 MW or 10 MW, was present at, respectively, 44% and 21% of the total duration of the flat-top stage of discharges. It is shown that large, ∼100% in magnitude, jumps of T _e at ρ = 0, caused by the switch-on of auxiliary heating, can be described with a ∼20% accuracy by the jumps of the space-averaged temperature if the DUP is used to describe the stationary shape of the temperature spatial profile. The results obtained illustrate the degree of plasma self-organization in tokamaks.

Data on the cross section and kinetic rate of charge exchange (CX) between the bare beryllium nucleus, the ion Be(+4) and the neutral hydrogen atom are of great interest for visible-range high-resolution spectroscopy in the ITER tokamak because beryllium is intended as the material for the first wall in the main chamber. Here an analysis of available data is presented, and the data needs are formulated. Besides the active probe signal produced by the CX of the diagnostic hydrogen neutral beam with impurity ions in plasma, a passive signal produced by the CX of impurity ions with cold edge plasma is also important, as it shows in observation data from the JET (Joint European Torus) tokamak with an ITER-like beryllium wall. Data in the range of a few eV/amu to ~100 eV/amu (amu stands for the atomic mass unit) needed for simulations of level populations for principal and orbital quantum numbers in the emitting beryllium ions Be(+3) can be obtained with the help of two-dimensional kinetic codes. The lack of literature data, especially for data resolved in orbital quantum numbers, has instigated us to make numerical calculations with the ARSENY code. A comparison of the results obtained for the one-centre Coulomb problem using an analytic approach and for the two-centre problem using numerical simulations is presented.

The study is stimulated by the expected noticeable deviation of the electron velocity distribution function (eVDF) from a Maxwellian under condition of a strong auxiliary heating of electron plasmas in tokamak-reactors. The key principles of accuracy estimation of the Thomson scattering diagnostic of non-Maxwellian plasmas in tokamak-reactors are presented. The algorithm extends the conventional approach to the assessment of non-Maxwellian plasmas measurements errors for a broad class of deviations of the eVDF from a Maxwellian. The algorithm is based on solving the inverse problem many times to determine main parameters of the eVDF with allowance for all possible sources of error and statistical variation of the input parameters of the problem. The method is applied to a preliminary analysis of the advantages of the formerly suggested use of various wavelengths of probing laser radiation in the Thomson diagnostics of non-Maxwellian plasma on the example of the core plasma Thomson scattering diagnostic system which is under design for ITER tokamak. The results obtained confirm the relevance of the diversification of the probing laser radiation wavelength.

A simple qualitative model of the influence of grouping of atomic levels on the radiation losses of impurity ions in a near-wall low temperature plasma is proposed using the example of line radiation losses when excited states are populated by impact excitation by plasma electrons. A comparison of the relevant data simulated by the ADAS codes for low-charge ions of argon, neon, and nitrogen ions confirms the predicted effects of possible underestimation or overestimation of radiation losses when the number of atomic levels taken into account in the simulation in the collisional-radiative model decreases.